Problem: Simplify the following expression: $k = \dfrac{25s + 5}{5r + 15} + \dfrac{30s - 25r}{5r + 15}$ You can assume $r,s,t \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{25s + 5 + 30s - 25r}{5r + 15}$ $k = \dfrac{55s + 5 - 25r}{5r + 15}$ The numerator and denominator have a common factor of $5$, so we can simplify $k = \dfrac{11s + 1 - 5r}{r + 3}$